Abstract

A method using a Fourier series is demonstrated to optimize an LED array for local dimming applications in liquid crystal display backlighting. The same optimization method is also suitable for LED displays in which the Moiré effect must be suppressed during photography with a minimum loss of spatial resolution. Initially, the angular intensity profile of a Lambertian LED is modelled when backlighting a Lambertian rear projection screen and compared to experimental data. An array of optimized LEDs and the resulting screen intensity pattern is then derived such that an intensity distribution with an intensity deviation of less than 2% is achieved. The angular intensity profile of the LED is modified using adjustable Fourier coefficients optimized according to an algorithm. The algorithm is designed to achieve an illuminated screen area of maximum size for a bounded LED backlight array to appear uniform in intensity to an observer. This Fourier series approach provides an elegant method to optimize the intensity profile of LED backlight arrays without the use of ray tracing.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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2018 (4)

H. Chen, J. Lee, B. Lin, S. Chen, and S. Wu, “Liquid crystal display and organic light-emitting diode display: present status and future perspectives,” Light: Sci. Appl. 7(3), 17168 (2018).
[Crossref]

G. Yoon, S. Bae, Y. Boklee, and J. Yoon, “Edge-lit LCD backlight unit for 2D local Dimming,” Opt. Express 26(16), 20802 (2018).
[Crossref]

G. Tan, Y. Huang, M. Li, S. Lee, and S. Wu, “High dynamic range liquid crystal displays with a mini-LED backlight,” Opt. Express 26(13), 16572–16584 (2018).
[Crossref]

Z. Zhao, H. Zhang, H. Zheng, and S. Liu, “New reversing freeform lens design method for LED uniform illumination with extended source and near field,” Opt. Commun. 410, 123–129 (2018).
[Crossref]

2017 (2)

Y. Shi, B. Li, M. Zhao, Y. Zhou, and D. Zhang, “The design of LED rectangular uniform illumination lens system,” Optik 144, 251–256 (2017).
[Crossref]

H. Chen, R. Zhu, M. Li, S. Lee, and S. Wu, “Pixel-by-pixel local dimming for high dynamic-range liquid crystal displays,” Opt. Express 25(3), 1973–1984 (2017).
[Crossref]

2016 (1)

2015 (3)

S. Hu, K. Du, T. Mei, L. Wan, and N. Zhu, “Ultra-compact LED lens with double freeform surfaces for uniform illumination,” Opt. Express 23(16), 20350–20355 (2015).
[Crossref]

H. Wu, X. Zhang, and P. Ge, “Double freeform surfaces lens design for LED uniform illumination with high distance–height ratio,” Opt. Laser Technol. 73, 166–172 (2015).
[Crossref]

K. Lin, N. Liao, D. Zhao, S. Dong, and Y. Li, “Analysis of Moiré minimization in color LED flat-panel display,” Proc. SPIE, 9618, 96180K (2015).
[Crossref]

2013 (1)

N. Burini, E. Nadernejad, J. Korhonen, S. Forchhammer, and X. Wu, “Modeling Power-Constrained Optimal Backlight Dimming for Color Displays,” J. Disp. Technol. 9(8), 656–665 (2013).
[Crossref]

2012 (1)

2011 (3)

K. wang, D. wu, Z. Qin, F. Chen, X. Luo, and S. Liu, “New reversing design method for LED uniform illumination,” Opt. Express 19(S4), A830–A840 (2011).
[Crossref]

A. J. Whang, S. Chao, C. Chen, Y. Chen, H. Hsiao, and X. Hu, “High Uniform Illumination of Light-Emitting Diodes Lighting with Applying the Multiple-Curvature Lens,” Opt. Rev. 18(2), 218–223 (2011).
[Crossref]

J. Korhonen, N. Burini, S. Forchhammer, and J. M. Pedersen, “Modeling LCD displays with local backlight dimming for image quality assessment,” Proc. SPIE 7866, 786607 (2011).
[Crossref]

2010 (2)

I. Moreno, “Illumination uniformity assessment based on human vision,” Opt. Lett. 35(23), 4030 (2010).
[Crossref]

T. Jung, M. Albrecht, C. Xu, and A. Karrenbauer, “P-56: Application of the SS C Local Dimming Algorithm for an Edge-Lit TV,” Soc. Inf. Disp. 41(1), 1450–1453 (2010).
[Crossref]

2009 (1)

D. DeAgazio, “Thin is In: LED Backlight Units Are Becoming Thinner and Brighter to Meet Consumer-Product Requirements,” Soc. Inf. Disp. 25(2), 16–20 (2009).
[Crossref]

2007 (1)

P. de Greef and H. G. Hulze, “Adaptive Dimming and Boosting Backlight for LCD-TV Systems,” Soc. Inf. Disp. 38(1), 1332–1335 (2007).
[Crossref]

1948 (1)

Albrecht, M.

T. Jung, M. Albrecht, C. Xu, and A. Karrenbauer, “P-56: Application of the SS C Local Dimming Algorithm for an Edge-Lit TV,” Soc. Inf. Disp. 41(1), 1450–1453 (2010).
[Crossref]

Bae, S.

Boklee, Y.

Burini, N.

N. Burini, E. Nadernejad, J. Korhonen, S. Forchhammer, and X. Wu, “Modeling Power-Constrained Optimal Backlight Dimming for Color Displays,” J. Disp. Technol. 9(8), 656–665 (2013).
[Crossref]

J. Korhonen, N. Burini, S. Forchhammer, and J. M. Pedersen, “Modeling LCD displays with local backlight dimming for image quality assessment,” Proc. SPIE 7866, 786607 (2011).
[Crossref]

Chao, S.

A. J. Whang, S. Chao, C. Chen, Y. Chen, H. Hsiao, and X. Hu, “High Uniform Illumination of Light-Emitting Diodes Lighting with Applying the Multiple-Curvature Lens,” Opt. Rev. 18(2), 218–223 (2011).
[Crossref]

Chen, C.

A. J. Whang, S. Chao, C. Chen, Y. Chen, H. Hsiao, and X. Hu, “High Uniform Illumination of Light-Emitting Diodes Lighting with Applying the Multiple-Curvature Lens,” Opt. Rev. 18(2), 218–223 (2011).
[Crossref]

Chen, F.

Chen, H.

H. Chen, J. Lee, B. Lin, S. Chen, and S. Wu, “Liquid crystal display and organic light-emitting diode display: present status and future perspectives,” Light: Sci. Appl. 7(3), 17168 (2018).
[Crossref]

H. Chen, R. Zhu, M. Li, S. Lee, and S. Wu, “Pixel-by-pixel local dimming for high dynamic-range liquid crystal displays,” Opt. Express 25(3), 1973–1984 (2017).
[Crossref]

H. Chen, J. Sung, T. Ha, Y. Park, and C. Hong, “Backlight Local Dimming Algorithm for High Contrast LCD-TV,” in Proc. ASID, New Delhi, India, Oct. 2006, pp. 168–171.

Chen, S.

H. Chen, J. Lee, B. Lin, S. Chen, and S. Wu, “Liquid crystal display and organic light-emitting diode display: present status and future perspectives,” Light: Sci. Appl. 7(3), 17168 (2018).
[Crossref]

Chen, Y.

A. J. Whang, S. Chao, C. Chen, Y. Chen, H. Hsiao, and X. Hu, “High Uniform Illumination of Light-Emitting Diodes Lighting with Applying the Multiple-Curvature Lens,” Opt. Rev. 18(2), 218–223 (2011).
[Crossref]

de Greef, P.

P. de Greef and H. G. Hulze, “Adaptive Dimming and Boosting Backlight for LCD-TV Systems,” Soc. Inf. Disp. 38(1), 1332–1335 (2007).
[Crossref]

DeAgazio, D.

D. DeAgazio, “Thin is In: LED Backlight Units Are Becoming Thinner and Brighter to Meet Consumer-Product Requirements,” Soc. Inf. Disp. 25(2), 16–20 (2009).
[Crossref]

Dong, S.

K. Lin, N. Liao, D. Zhao, S. Dong, and Y. Li, “Analysis of Moiré minimization in color LED flat-panel display,” Proc. SPIE, 9618, 96180K (2015).
[Crossref]

Du, K.

Forchhammer, S.

N. Burini, E. Nadernejad, J. Korhonen, S. Forchhammer, and X. Wu, “Modeling Power-Constrained Optimal Backlight Dimming for Color Displays,” J. Disp. Technol. 9(8), 656–665 (2013).
[Crossref]

J. Korhonen, N. Burini, S. Forchhammer, and J. M. Pedersen, “Modeling LCD displays with local backlight dimming for image quality assessment,” Proc. SPIE 7866, 786607 (2011).
[Crossref]

X. Shu, X. Wu, and S. Forchhammer, “Optimal local dimming for LED backlit LCD displays via linear programming,” Proc. SPIE8305, 83050K (2012).
[Crossref]

Ge, P.

H. Wu, X. Zhang, and P. Ge, “Double freeform surfaces lens design for LED uniform illumination with high distance–height ratio,” Opt. Laser Technol. 73, 166–172 (2015).
[Crossref]

Ha, T.

H. Chen, J. Sung, T. Ha, Y. Park, and C. Hong, “Backlight Local Dimming Algorithm for High Contrast LCD-TV,” in Proc. ASID, New Delhi, India, Oct. 2006, pp. 168–171.

Hong, C.

H. Chen, J. Sung, T. Ha, Y. Park, and C. Hong, “Backlight Local Dimming Algorithm for High Contrast LCD-TV,” in Proc. ASID, New Delhi, India, Oct. 2006, pp. 168–171.

Hsiao, H.

A. J. Whang, S. Chao, C. Chen, Y. Chen, H. Hsiao, and X. Hu, “High Uniform Illumination of Light-Emitting Diodes Lighting with Applying the Multiple-Curvature Lens,” Opt. Rev. 18(2), 218–223 (2011).
[Crossref]

Hu, S.

Hu, X.

A. J. Whang, S. Chao, C. Chen, Y. Chen, H. Hsiao, and X. Hu, “High Uniform Illumination of Light-Emitting Diodes Lighting with Applying the Multiple-Curvature Lens,” Opt. Rev. 18(2), 218–223 (2011).
[Crossref]

Huang, Y.

Hulze, H. G.

P. de Greef and H. G. Hulze, “Adaptive Dimming and Boosting Backlight for LCD-TV Systems,” Soc. Inf. Disp. 38(1), 1332–1335 (2007).
[Crossref]

Ji, C.

Jung, T.

T. Jung, M. Albrecht, C. Xu, and A. Karrenbauer, “P-56: Application of the SS C Local Dimming Algorithm for an Edge-Lit TV,” Soc. Inf. Disp. 41(1), 1450–1453 (2010).
[Crossref]

Karrenbauer, A.

T. Jung, M. Albrecht, C. Xu, and A. Karrenbauer, “P-56: Application of the SS C Local Dimming Algorithm for an Edge-Lit TV,” Soc. Inf. Disp. 41(1), 1450–1453 (2010).
[Crossref]

Korhonen, J.

N. Burini, E. Nadernejad, J. Korhonen, S. Forchhammer, and X. Wu, “Modeling Power-Constrained Optimal Backlight Dimming for Color Displays,” J. Disp. Technol. 9(8), 656–665 (2013).
[Crossref]

J. Korhonen, N. Burini, S. Forchhammer, and J. M. Pedersen, “Modeling LCD displays with local backlight dimming for image quality assessment,” Proc. SPIE 7866, 786607 (2011).
[Crossref]

Lee, J.

H. Chen, J. Lee, B. Lin, S. Chen, and S. Wu, “Liquid crystal display and organic light-emitting diode display: present status and future perspectives,” Light: Sci. Appl. 7(3), 17168 (2018).
[Crossref]

Lee, S.

Lee, S. G.

Li, B.

Y. Shi, B. Li, M. Zhao, Y. Zhou, and D. Zhang, “The design of LED rectangular uniform illumination lens system,” Optik 144, 251–256 (2017).
[Crossref]

Li, M.

Li, Y.

K. Lin, N. Liao, D. Zhao, S. Dong, and Y. Li, “Analysis of Moiré minimization in color LED flat-panel display,” Proc. SPIE, 9618, 96180K (2015).
[Crossref]

Liao, N.

K. Lin, N. Liao, D. Zhao, S. Dong, and Y. Li, “Analysis of Moiré minimization in color LED flat-panel display,” Proc. SPIE, 9618, 96180K (2015).
[Crossref]

Lin, B.

H. Chen, J. Lee, B. Lin, S. Chen, and S. Wu, “Liquid crystal display and organic light-emitting diode display: present status and future perspectives,” Light: Sci. Appl. 7(3), 17168 (2018).
[Crossref]

Lin, K.

K. Lin, N. Liao, D. Zhao, S. Dong, and Y. Li, “Analysis of Moiré minimization in color LED flat-panel display,” Proc. SPIE, 9618, 96180K (2015).
[Crossref]

Liu, S.

Luo, X.

Mei, T.

Moreno, I.

Nadernejad, E.

N. Burini, E. Nadernejad, J. Korhonen, S. Forchhammer, and X. Wu, “Modeling Power-Constrained Optimal Backlight Dimming for Color Displays,” J. Disp. Technol. 9(8), 656–665 (2013).
[Crossref]

Park, B. O. S.

Park, J.

Park, Y.

H. Chen, J. Sung, T. Ha, Y. Park, and C. Hong, “Backlight Local Dimming Algorithm for High Contrast LCD-TV,” in Proc. ASID, New Delhi, India, Oct. 2006, pp. 168–171.

Pedersen, J. M.

J. Korhonen, N. Burini, S. Forchhammer, and J. M. Pedersen, “Modeling LCD displays with local backlight dimming for image quality assessment,” Proc. SPIE 7866, 786607 (2011).
[Crossref]

Qin, Z.

Quin, Z.

Rose, A.

Shi, Y.

Y. Shi, B. Li, M. Zhao, Y. Zhou, and D. Zhang, “The design of LED rectangular uniform illumination lens system,” Optik 144, 251–256 (2017).
[Crossref]

Shu, X.

X. Shu, X. Wu, and S. Forchhammer, “Optimal local dimming for LED backlit LCD displays via linear programming,” Proc. SPIE8305, 83050K (2012).
[Crossref]

Sung, J.

H. Chen, J. Sung, T. Ha, Y. Park, and C. Hong, “Backlight Local Dimming Algorithm for High Contrast LCD-TV,” in Proc. ASID, New Delhi, India, Oct. 2006, pp. 168–171.

Tan, G.

Wan, L.

Wang, K.

Whang, A. J.

A. J. Whang, S. Chao, C. Chen, Y. Chen, H. Hsiao, and X. Hu, “High Uniform Illumination of Light-Emitting Diodes Lighting with Applying the Multiple-Curvature Lens,” Opt. Rev. 18(2), 218–223 (2011).
[Crossref]

wu, D.

Wu, H.

H. Wu, X. Zhang, and P. Ge, “Double freeform surfaces lens design for LED uniform illumination with high distance–height ratio,” Opt. Laser Technol. 73, 166–172 (2015).
[Crossref]

Wu, S.

Wu, X.

N. Burini, E. Nadernejad, J. Korhonen, S. Forchhammer, and X. Wu, “Modeling Power-Constrained Optimal Backlight Dimming for Color Displays,” J. Disp. Technol. 9(8), 656–665 (2013).
[Crossref]

X. Shu, X. Wu, and S. Forchhammer, “Optimal local dimming for LED backlit LCD displays via linear programming,” Proc. SPIE8305, 83050K (2012).
[Crossref]

Xu, C.

T. Jung, M. Albrecht, C. Xu, and A. Karrenbauer, “P-56: Application of the SS C Local Dimming Algorithm for an Edge-Lit TV,” Soc. Inf. Disp. 41(1), 1450–1453 (2010).
[Crossref]

Yang, J. S.

Yoon, G.

Yoon, J.

Zhang, D.

Y. Shi, B. Li, M. Zhao, Y. Zhou, and D. Zhang, “The design of LED rectangular uniform illumination lens system,” Optik 144, 251–256 (2017).
[Crossref]

Zhang, H.

Z. Zhao, H. Zhang, H. Zheng, and S. Liu, “New reversing freeform lens design method for LED uniform illumination with extended source and near field,” Opt. Commun. 410, 123–129 (2018).
[Crossref]

Zhang, X.

H. Wu, X. Zhang, and P. Ge, “Double freeform surfaces lens design for LED uniform illumination with high distance–height ratio,” Opt. Laser Technol. 73, 166–172 (2015).
[Crossref]

Zhao, D.

K. Lin, N. Liao, D. Zhao, S. Dong, and Y. Li, “Analysis of Moiré minimization in color LED flat-panel display,” Proc. SPIE, 9618, 96180K (2015).
[Crossref]

Zhao, M.

Y. Shi, B. Li, M. Zhao, Y. Zhou, and D. Zhang, “The design of LED rectangular uniform illumination lens system,” Optik 144, 251–256 (2017).
[Crossref]

Zhao, Z.

Z. Zhao, H. Zhang, H. Zheng, and S. Liu, “New reversing freeform lens design method for LED uniform illumination with extended source and near field,” Opt. Commun. 410, 123–129 (2018).
[Crossref]

Zheng, H.

Z. Zhao, H. Zhang, H. Zheng, and S. Liu, “New reversing freeform lens design method for LED uniform illumination with extended source and near field,” Opt. Commun. 410, 123–129 (2018).
[Crossref]

Zhou, Y.

Y. Shi, B. Li, M. Zhao, Y. Zhou, and D. Zhang, “The design of LED rectangular uniform illumination lens system,” Optik 144, 251–256 (2017).
[Crossref]

Zhu, N.

Zhu, R.

J. Disp. Technol. (1)

N. Burini, E. Nadernejad, J. Korhonen, S. Forchhammer, and X. Wu, “Modeling Power-Constrained Optimal Backlight Dimming for Color Displays,” J. Disp. Technol. 9(8), 656–665 (2013).
[Crossref]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Korea (1)

Light: Sci. Appl. (1)

H. Chen, J. Lee, B. Lin, S. Chen, and S. Wu, “Liquid crystal display and organic light-emitting diode display: present status and future perspectives,” Light: Sci. Appl. 7(3), 17168 (2018).
[Crossref]

Opt. Commun. (1)

Z. Zhao, H. Zhang, H. Zheng, and S. Liu, “New reversing freeform lens design method for LED uniform illumination with extended source and near field,” Opt. Commun. 410, 123–129 (2018).
[Crossref]

Opt. Express (6)

Opt. Laser Technol. (1)

H. Wu, X. Zhang, and P. Ge, “Double freeform surfaces lens design for LED uniform illumination with high distance–height ratio,” Opt. Laser Technol. 73, 166–172 (2015).
[Crossref]

Opt. Lett. (1)

Opt. Rev. (1)

A. J. Whang, S. Chao, C. Chen, Y. Chen, H. Hsiao, and X. Hu, “High Uniform Illumination of Light-Emitting Diodes Lighting with Applying the Multiple-Curvature Lens,” Opt. Rev. 18(2), 218–223 (2011).
[Crossref]

Optik (1)

Y. Shi, B. Li, M. Zhao, Y. Zhou, and D. Zhang, “The design of LED rectangular uniform illumination lens system,” Optik 144, 251–256 (2017).
[Crossref]

Proc. SPIE (2)

K. Lin, N. Liao, D. Zhao, S. Dong, and Y. Li, “Analysis of Moiré minimization in color LED flat-panel display,” Proc. SPIE, 9618, 96180K (2015).
[Crossref]

J. Korhonen, N. Burini, S. Forchhammer, and J. M. Pedersen, “Modeling LCD displays with local backlight dimming for image quality assessment,” Proc. SPIE 7866, 786607 (2011).
[Crossref]

Soc. Inf. Disp. (3)

T. Jung, M. Albrecht, C. Xu, and A. Karrenbauer, “P-56: Application of the SS C Local Dimming Algorithm for an Edge-Lit TV,” Soc. Inf. Disp. 41(1), 1450–1453 (2010).
[Crossref]

P. de Greef and H. G. Hulze, “Adaptive Dimming and Boosting Backlight for LCD-TV Systems,” Soc. Inf. Disp. 38(1), 1332–1335 (2007).
[Crossref]

D. DeAgazio, “Thin is In: LED Backlight Units Are Becoming Thinner and Brighter to Meet Consumer-Product Requirements,” Soc. Inf. Disp. 25(2), 16–20 (2009).
[Crossref]

Other (2)

X. Shu, X. Wu, and S. Forchhammer, “Optimal local dimming for LED backlit LCD displays via linear programming,” Proc. SPIE8305, 83050K (2012).
[Crossref]

H. Chen, J. Sung, T. Ha, Y. Park, and C. Hong, “Backlight Local Dimming Algorithm for High Contrast LCD-TV,” in Proc. ASID, New Delhi, India, Oct. 2006, pp. 168–171.

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Figures (18)

Fig. 1.
Fig. 1. LED array pattern on a screen due to an LED backlight located 3 cm behind the screen. LED pitch is 4.96 cm and each LED is a Lambertian emitter.
Fig. 2.
Fig. 2. Intensity profile of a Lambertian source, using both Polar coordinates (Left), and Cartesian coordinates (Right).
Fig. 3.
Fig. 3. Lambertian surface A: Ideal Diffuse transmittance, B: transmittance with directional component (non Lambertian)
Fig. 4.
Fig. 4. Diagram depicting intensity on a screen due to an LED as a function of θ
Fig. 5.
Fig. 5. Expected screen intensity versus angle θ from Eq. (2). Both LED and screen are assumed Lambertian, and θ is defined in Fig. 3.
Fig. 6.
Fig. 6. Relationship between Io and I due to LED- screen distance
Fig. 7.
Fig. 7. Subtended screen area versus θ
Fig. 8.
Fig. 8. Overlap of 2 adjacent LEDs and the resulting intensity profile (green) that an observer would see on a screen due to 2 LEDs. The difference between the two peaks and the valley between them is 34.28% of the intensity of the peak. x is defined in Fig. 7
Fig. 9.
Fig. 9. Spatial percent deviation in luminous intensity as a function of screen height for various spacing between two adjacent LEDs
Fig. 10.
Fig. 10. Window uniformity is defined by screen area over which uniformity may be achieved (red) in this example overlaying an 8 × 8 LED array. Outside of the window, screen illumination will drop off rapidly and deviates by more than +/- 1%.
Fig. 11.
Fig. 11. Intensity profile of XQ-E high Intensity LED on a screen; Photometer results (green), Theory of Eq. (2) (blue), Camera results (red)
Fig. 12.
Fig. 12. A) actual LED array, B) LED array model, both viewed after a screen.
Fig. 13.
Fig. 13. Lambertian Intensity profile of cos4θ (blue) compared to the new optimized intensity profile (red)
Fig. 14.
Fig. 14. (Left) 20 × 20 LED array with Lambertian LED distribution.
Fig. 15.
Fig. 15. (right) 20 × 20 LED array using Fourier coefficients from Table 1 for each LED
Fig. 16.
Fig. 16. Topographical percent deviation of the uniformity of the screen in Fig. 15
Fig. 17.
Fig. 17. Window of uniformity (yellow) edges of the LED array (pink)
Fig. 18.
Fig. 18. Visually analyzing how increasing R affects bloom. The first row depicts a cross section of the intensity profile of a 20 × 20 LED array. The bottom row shows a top down view as an observer would see on a Lambertian screen.

Tables (1)

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Table 1. Fourier coefficients determined via Matlab algorithm.

Equations (10)

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ILED=I0cosθ
IScreen=I0cos4θ
I01D2,I1H2,I=I0(DH)2
dy=dxcosθ
F(α)=a02+n=1[ancos(nπαp)+bnsin(nπαp)]
an=1pppf(α)cos(nπαp)dα
bn=1pppf(α)sin(nπαp)dα
I=cos4θ=38+12cos(2θ)+18cos(4θ)
Ioptimized=a0+a1cos(2θ)+a2cos(4θ)+a3cos(6θ)+a4cos(8θ)+
R=DeviationParameterWindowSize

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